You own shares in the XYZ company.For the first 10 years that you owned the shares,they paid a dividend of $150 every 6 months (paid at the end of every 6 months).However due to a downturn in the economy,no dividend has been paid in the past 2 years.If you have reinvested the dividends in a fund earning j₂ = 5%,how much do you have today? A)$4229.48 B)$4224.45 C)$4126.32 D)$3831.70

Question

Quizplus · Accepted Answer

The dividends were reinvested in a fund earning 5% annually, so we use the formula for the future value of an annuity to calculate the total amount. The dividends were $150 every 6 months for 10 years, which is 20 periods. The interest rate per period (semi-annually) is 2.5% (half of 5%). The future value of an annuity formula is $FV = P \times \frac{(1 + r)^n - 1}{r}$, where P is the payment ($150), r is the interest rate per period (0.025), and n is the total number of payments (20). Plugging in the values, we get $FV = 150 \times \frac{(1 + 0.025)^{20} - 1}{0.025}$, which calculates to approximately $4229.48.

You Own Shares in the XYZ Company